As h->0, show that(explain why)
sin(x+h) = sinx +hcosx + o(h)
some thing like this always depends on what you already know and are allowed to use.
If you know that the derivative of sin x is cos x, then you can find the tangent line to sin x at :
Taking , and, replacing with x,
sin(x+ h)= cos(x)h+ sin(x).
Another way would be to use the Taylor's series for sin(x) and cos(x):
Sorry person who is apparently not that awesome at maths.
"The above equation is wrong. The function on the LHS is the sine
function, whereas on the RHS you have a straight line. How can they
equal?
The tangent line is NOT equal to the curve. They only meet at ONE point:
the touching point."
Could someone else do my question?....
Do you know that if then where the o(1) is as ? Write down the difference quotient and use this to turn it into the tangent line estimate , then set f(x) = sin(x).
Also, be nice.
edit: Or were you trying to prove that the derivative of sine is the cosine?